Statistics for Experimenters

Binomial distribtuion

best example is a coin toss, its either heads or tails

mean ([math]\displaystyle{ \mu }[/math]) = number of tries [math]\displaystyle{ n }[/math](coin flips) * probability of success[math]\displaystyle{ p }[/math] (head, 1/2)

standard deviation([math]\displaystyle{ \sigma }[/math]) = [math]\displaystyle{ np(1-p) }[/math]

Poisson Distribution

standard deviation ([math]\displaystyle{ \sigma }[/math]) = root of the mean ([math]\displaystyle{ \sqrt{\mu} }[/math])

use in counting experiments

the distribtuion approximates the Binomial Distribution for the special case when the mean ([math]\displaystyle{ \mu }[/math]) is a lot less than the number of attempts to measure ([math]\displaystyle{ n }[/math]) because the probability of the event occurrring is small.

In the cosmic ray telescope experiment the mean number of detected cosmic rays is much smaller than the number of cosmic rays passing by.

Gaussian/Normal Distribution

Full WIdth at Half Max (FWHM) = width of the distribution at half the value of the maximum probabilty (distibution peak) = [math]\displaystyle{ \Gamma }[/math]

standard deviation ([math]\displaystyle{ \sigma }[/math]) = [math]\displaystyle{ \frac{\Gamma} {2.354} }[/math]

error = [math]\displaystyle{ 0.675 \sigma }[/math]